Question

A physics class has 40 students. Of these,14 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major.

The probability that a randomly selected student is female or a physics major is___. (Round to 3 decimal places)

Answer 1

Answer:

0.65 or 65%

Step-by-step explanation:

Students in class (n) = 40

Physics majors (P) = 14

Female students (F) = 18

Female Physics majors (P and F) = 6

The probability that a randomly selected student is female or a physics major is given by the probability that the student is female, added to the probability that the student is a physics major, subtracted by the probability of the student being a female physics major:

$P(F\ or\ P) = P(F)+P(P) - P(F\ and\ P)\\P(F\ or\ P) =\frac{14}{40}+\frac{18}{40}-\frac{6}{40}\\P(F\ or\ P) =0.65 = 65\%$

The probability that a randomly selected student is female or a physics major is 0.65 or 65%.